One of the first things you learn when starting a meditation practice is that fighting the thoughts that inevitably pop up only serves to amplify them. Like blowing air into a smoldering fire to put it out, trying to stop the mental interruptions typically has the opposite effect.
Swiss psychologist Carl Jung understood this paradox of mindfulness when he said "What you resist not only persists, but will grow in size."
When you sit in stillness, the best way to quiet the mind isn't to try to push thoughts away — it's to welcome them. Embrace thoughts. Then gently release them and return your attention to the breath or other object of focus.
If you do that, you'll often find that the mind gets quieter on its own. Sometimes, simply letting dust settle is better than sweeping it to the side.
Or as Alan Watts said, "Muddy water is best cleared by leaving it alone."